Dynamics of the 3-D fractional complex Ginzburg-Landau equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Lu, Hong^1,2,3  Bates, Peter W.³  Lu, Shujuan^1,2  Zhang, Mingji^3,4 

[1] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

[2] Beihang Univ, LMIB, Beijing 100191, Peoples R China

[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[4] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA

关键词: Fractional Ginzburg-Landau equation;    Global smooth solution;    Global attractor;    Hausdorff dimension;    Fractal dimension;   

DOI  :  10.1016/j.jde.2015.06.028

来源: Elsevier

【 摘 要 】

We study the initial boundary value problem of the fractional complex Ginzburg Landau equation in three spatial dimensions with the dissipative effect given by a fractional Laplacian. A priori estimates are derived when the nonlinearity satisfies certain growth conditions. Using Galerkin's method, the existence of a global smooth solution is established. Uniqueness is also proved. Furthermore, the existence of a global attractor is proved, and estimates of the Hausdorff and fractal dimensions for the global attractor are obtained. (C) 2015 Elsevier Inc. All rights reserved.

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